Instructions

Directions for the next 2 questions:

For a real number x, let

$$f(x) = 1/(1+x),$$ if $$x$$ is non-negative
$$f(x) = 1+x,$$ if $$x$$ is negative

$$f^n(x) = f(f^{n-1}(x)), n = 2, 3.....$$

Question 125

What is the value of the product, $$f(2) f^2(2)f^3(2) f^4(2)f^5(2)$$?

Solution

f(2) = 1/3

$$f^2(2)$$ = f(1/3) = 3/4

$$f^3(2)$$ = f(3/4) = 4/7

$$f^4(2)$$ = f(4/7) = 7/11

$$f^5(2)$$ = f(7/11) = 11/18

So, product = 1/18

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